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Item Selection By “Hub-Authority” Profit Ranking. Ke Wang Ming-Yen Thomas Su Simon Fraser University. Item Selection By “Hub-Authority” Profit Ranking. Ke Wang Ming-Yen Thomas Su Simon Fraser University. Ranking in Inter-related World. Web pages Social networks Cross sellings.

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item selection by hub authority profit ranking

Item Selection By “Hub-Authority” Profit Ranking

Ke Wang

Ming-Yen Thomas Su

Simon Fraser University

item selection by hub authority profit ranking1

Item Selection By “Hub-Authority” Profit Ranking

Ke Wang

Ming-Yen Thomas Su

Simon Fraser University

ranking in inter related world
Ranking in Inter-related World
  • Web pages
  • Social networks
  • Cross sellings
item ranking with cross selling effect
Item Ranking with Cross-selling Effect
  • What are the most profitable items?

100%

$10

$8

$5

60%

50%

35%

$3

$1.5

100%

$3

$0.5

30%

$2

$15

the hub authority modeling
The Hub/Authority Modeling
  • Hubs i: “introductory” for sales of other items j (i->j).
  • Authorities j: “necessary” for sales of other items i (i->j).
  • Solution: model the mutual enforcement of hub and authority weights through links.
    • Challenges: Incorporate individual profits of items and strength of links, and ensure hub/authority weights converges
selecting most profitable items
Selecting Most Profitable Items
  • Size-constrained selection
    • given a size s, find s items that produce the most profit as a whole
    • solution: select the s items at the top of ranking
  • Cost-constrained selection
    • given the cost for selecting each item, find a collection of items that produce the most profit as a whole
    • solution: the same as above for uniform cost
solution to const constrained selection

Estimated profit

Selection cost

Optimal cutoff

# of items selected

Solution to const-constrained selection
web page ranking algorithm hits hyperlink induced topic search
Web Page Ranking Algorithm – HITS (Hyperlink-Induced Topic Search)
  • Mutually reinforcing relationship
    • Hub weight: h(i) =  a(j), for all page j such that i have a link to j
    • Authority weight: a(i) =  h(j), for all page j that have a link to i h(j)
  • a and h converge if normalized before each iteration
the cross selling graph
The Cross-Selling Graph
  • Find frequent items and 2-itemsets
  • Create a link i  j if Conf(i  j) is above a specified value (i and j may be same)
  • “Quality” of link i j: prof(i)*conf(i j). Intuitively, it is the credit of j due to its influence on i
computing weights in hap
Computing Weights in HAP
  • For each iteration,
    • Authority weights: a(i) =  j  i prof(j) conf(j  i)  h(j)
    • Hub weights: h(i) =  i  j prof(i) conf(i  j)  a(i)
  • Cross-selling matrix B
    • B[i, j] = prof(i)  conf(i, j) for link i j
    • B[i, j]=0 if no link i j (i.e. (i, j) is not frequent set)
  • Compute weights iteratively or use eigen analysis
  • Rank items using their authority weights
example
Example
  • Given frequent items, X, Y, and Z and the table
  • We get the cross-selling matrix B:

e.g. B[X,Y] = prof(X)  conf(X,Y) = 1.0000

example con t
Example (con’t)
  • prof(X) = $5, prof(Y) = $1, prof(Z) = $0.1
  • a(X) = 0.767, a(Y) = 0.166, a(Z) = 0.620
  • HAP Ranking is different from ranking the individual profit
    • The cross-selling effect increases the profitability of Z
empirical study
Empirical Study
  • Conduct experiments on two datasets
  • Compare 3 selection methods: HAP, PROFSET [4, 5], and Naïve.
  • HAP generate the highest estimated profit in most cases.